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Sergeeva-Olga [200]
3 years ago
10

Write down in terms of n, an expression for the nth term

Mathematics
2 answers:
Hatshy [7]3 years ago
8 0

Answer:

The nth term will be:

a_n=-5n+30

Step-by-step explanation:

Given the sequence

25, 20, 15, 10, 5​

An Arithmetic sequence has a constant difference 'd' and is defined by

a_n=a_1+\left(n-1\right)d

Computing the common difference of all the adjacent terms

25,\:20,\:15,\:10,\:5

20-25=-5,\:\quad \:15-20=-5,\:\quad \:10-15=-5,\:\quad \:5-10=-5

As the difference between all the adjacent terms is the same and equal to

d=-5

Also, the first term is:

a_1=25

Hence, the nth term will be:

a_n=a_1+\left(n-1\right)d

a_n=-5\left(n-1\right)+25        ∵ a_1=25, d=-5

a_n=-5n+30

Therefore, the nth term will be:

a_n=-5n+30

pshichka [43]3 years ago
5 0

Answer:

Solution,

First term (a) = 25

Common difference (d) = Second term - first term = 20 - 25 = -5

Now,

nth term = a + (n - 1)d = 25 + (n - 1) (-5) = 25 - 5n +5 = 30 - 5n

The nth term of the series is 30 - 5n

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What is the volume of a sphere with a radius of 7mm
elena-14-01-66 [18.8K]
1)  The answer, in terms of  "π", is:
_________________________________
  "  (\frac{1372 mm^3}{3}) *  π    mm³ " .
___________________________________________________
2) The answer, using "3.14" for "π", is:
___________________________________________________
" 1436.0266666666666667  mm³ " ; round to: " 1436.027 mm³ " ; 

        or; write as: " 1436 \frac{2}{75}  mm³ " .
___________________________________________________
Explanation: 
____________________________________________
The formula for the volume, "V" of a sphere is:

V = \frac{4}{3} * π* r³ ;

in which "r" = radius = "7 mm" {given}.

We can solve using "3.14" for "π" ; or we can solve in terms of "π" ;
_________________________________________
1)  In terms of "π" :
_________________________________________
   V = \frac{4}{3} * π * r³ ;

      = \frac{4}{3} * π * (7 mm)³ ;

      = \frac{4}{3} * π * (7 * 7 * 7 * mm³) ;
 
      = \frac{4}{3} * π * (49 * 7 * mm³) ;

      = \frac{4}{3} * π * (343 mm³) ;

      = \frac{4* 343 mm^3}{3}) * π   mm³

      =  (\frac{1372 mm^3}{3}) *  π    mm³  ;

________________________________________________________
2)  Using "3.14" for "π" :
________________________________________________________
     V = \frac{4}{3} * π * r³ ; 

        = \frac{4}{3} * (3.14)* (7 mm)³ ;

        = \frac{4}{3} * (3.14) * (7 * 7 * 7 * mm³) ;

        = \frac{4}{3} * (3.14) * (49 * 7 * mm³) ;

        = \frac{4}{3} * (3.14) * (49 * 7 * mm³) ;

        = \frac{4}{3} * (3.14)  * (343 mm³) ;

        = { \frac{4}{3} }  * (3.14 * 343 mm³) ;

        = { \frac{4}{3} } *  (1077.02 mm³) ;

        = (4 * 1077.02 mm³) / 3 ; 

        = (4308.08 mm³) / 3 ; 
__________________________________________________________
        =  1436.0266666666666667  mm³ ;  round to: " 1436.027 mm³ " ;

        or; write as: " 1436 \frac{2}{75}  mm³ " .
__________________________________________________________
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